Square Root of 1368
2026-02-28 12:45 Diff
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Last updated on August 5, 2025

If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1368.

What is the Square Root of 1368?

The square root is the inverse of the square of a number. 1368 is not a perfect square. The square root of 1368 is expressed in both radical and exponential form. In the radical form, it is expressed as √1368, whereas (1368)^(1/2) in the exponential form. √1368 ≈ 36.9858, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 1368

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where the long division method and approximation method are used. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 1368 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1368 is broken down into its prime factors.

Step 1: Finding the prime factors of 1368.

Breaking it down, we get 2 × 2 × 2 × 3 × 3 × 19: 2^3 × 3^2 × 19

Step 2: Now that we have found the prime factors of 1368, the second step is to make pairs of those prime factors. Since 1368 is not a perfect square, the digits of the number can’t be fully grouped in pairs. Therefore, calculating 1368 using prime factorization is limited in providing an exact integer result.

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Square Root of 1368 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 1368, we need to group it as 68 and 13.

Step 2: Now we need to find n whose square is less than or equal to 13. We can say n is '3' because 3 × 3 = 9 is less than or equal to 13. Now the quotient is 3, after subtracting 9 from 13, the remainder is 4.

Step 3: Bring down 68, making the new dividend 468. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.

Step 4: The new divisor is 6n. We need to find n such that 6n × n ≤ 468. Let n be 7, then 67 × 7 = 469 which is slightly more than 468. Let's use n = 6, 66 × 6 = 396.

Step 5: Subtract 396 from 468, the difference is 72, and the quotient is 36.

Step 6: Add a decimal point to continue the division and bring down two zeros to the remainder, making it 7200.

Step 7: Find the next divisor. Use the quotient 369, so 369n ≤ 7200. Find suitable n; let's say n = 1, 369 × 1 = 369.

Step 8: Continue the division until the desired accuracy is reached. So the square root of √1368 is approximately 36.98.

Square Root of 1368 by Approximation Method

The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1368 using the approximation method.

Step 1: Find the closest perfect squares around √1368. The smallest perfect square less than 1368 is 1296 (36^2) and the largest perfect square more than 1368 is 1444 (38^2). √1368 falls between 36 and 38.

Step 2: Apply the formula: (Given number - smaller perfect square) ÷ (larger perfect square - smaller perfect square). Using the formula: (1368 - 1296) ÷ (1444 - 1296) = 72 ÷ 148 ≈ 0.486 Add this decimal to the lower integer square root: 36 + 0.486 = 36.486, so the square root of 1368 is approximately 36.49.

Common Mistakes and How to Avoid Them in the Square Root of 1368

Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. Now let us look at a few of those mistakes that students tend to make in detail.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √1368?

Okay, lets begin

The area of the square is approximately 1368 square units.

Explanation

The area of the square = side^2.

The side length is given as √1368.

Area of the square = side^2 = √1368 × √1368 = 1368.

Therefore, the area of the square box is approximately 1368 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1368 square feet is built; if each of the sides is √1368, what will be the square feet of half of the building?

Okay, lets begin

684 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 1368 by 2 = we get 684.

So half of the building measures 684 square feet.

Well explained 👍

Problem 3

Calculate √1368 × 5.

Okay, lets begin

Approximately 184.93

Explanation

The first step is to find the square root of 1368, which is approximately 36.98.

The second step is to multiply 36.98 by 5.

So, 36.98 × 5 ≈ 184.93

Well explained 👍

Problem 4

What will be the square root of (1368 + 32)?

Okay, lets begin

The square root is approximately 38.

Explanation

To find the square root, we need to find the sum of (1368 + 32). 1368 + 32 = 1400, and then √1400 ≈ 37.42.

Therefore, the square root of (1368 + 32) is approximately 37.42.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1368 units and the width ‘w’ is 40 units.

Okay, lets begin

The perimeter of the rectangle is approximately 153.96 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√1368 + 40) = 2 × (36.98 + 40) = 2 × 76.98 ≈ 153.96 units.

Well explained 👍

FAQ on Square Root of 1368

1.What is √1368 in its simplest form?

The prime factorization of 1368 is 2 × 2 × 2 × 3 × 3 × 19. The simplest form of √1368 = √(2 × 2 × 2 × 3 × 3 × 19).

2.Mention the factors of 1368.

Factors of 1368 are 1, 2, 3, 4, 6, 8, 9, 12, 19, 24, 27, 36, 38, 57, 72, 76, 114, 152, 171, 228, 342, 456, 684, and 1368.

3.Calculate the square of 1368.

We get the square of 1368 by multiplying the number by itself, that is 1368 × 1368 = 1,872,624.

4.Is 1368 a prime number?

1368 is not a prime number, as it has more than two factors.

5.1368 is divisible by?

1368 has many factors; those are 1, 2, 3, 4, 6, 8, 9, 12, 19, 24, 27, 36, 38, 57, 72, 76, 114, 152, 171, 228, 342, 456, 684, and 1368.

Important Glossaries for the Square Root of 1368

  • Square root: A square root of a number is a value that, when multiplied by itself, gives the original number. Example: 6^2 = 36, and the square root is √36 = 6.
  • Irrational number: An irrational number is a number that cannot be expressed as a simple fraction; its decimal goes on forever without repeating.
  • Approximation: The process of finding a value that is close enough to the correct answer, usually within a specified tolerance.
  • Perfect square: A number that is the square of an integer. Example: 36 is a perfect square because it is 6^2.
  • Prime factorization: Expressing a number as the product of its prime factors. Example: The prime factorization of 1368 is 2^3 × 3^2 × 19.

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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